On minimality of convolutional ring encoders

Details On minimality of convolutional ring encoders On minimality of convolutional ring encoders

2008-01-24

arxiv.org/abs/0801.3703v2

IEEE Trans. Information Theory, Vol. 55, No. 11, pp. 4890-4897, November 2009

Computer Science

Information Theory

13 pages in v1, submitted; 8 pages in revision v2

Scientific paper

Convolutional codes are considered with code sequences modelled as semi-infinite Laurent series. It is wellknown that a convolutional code C over a finite group G has a minimal trellis representation that can be derived from code sequences. It is also wellknown that, for the case that G is a finite field, any polynomial encoder of C can be algebraically manipulated to yield a minimal polynomial encoder whose controller canonical realization is a minimal trellis. In this paper we seek to extend this result to the finite ring case G = Z_{p^r} by introducing a socalled "p-encoder". We show how to manipulate a polynomial encoding of a noncatastrophic convolutional code over Z_{p^r} to produce a particular type of p-encoder ("minimal p-encoder") whose controller canonical realization is a minimal trellis with nonlinear features. The minimum number of trellis states is then expressed as p^gamma, where gamma is the sum of the row degrees of the minimal p-encoder. In particular, we show that any convolutional code over Z_{p^r} admits a delay-free p-encoder which implies the novel result that delay-freeness is not a property of the code but of the encoder, just as in the field case. We conjecture that a similar result holds with respect to catastrophicity, i.e., any catastrophic convolutional code over Z_{p^r} admits a noncatastrophic p-encoder.

Affiliated with

Also associated with

No associations

Rating

On minimality of convolutional ring encoders does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On minimality of convolutional ring encoders, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On minimality of convolutional ring encoders will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-282966